for the pair of functions f(x)=^2+4 and g(x)=x+5, find the following

a).(f*g)(x) b).(f*g)(2) c).(g*f)(x) d).(g*f)(2)

Question

for the pair of functions f(x)=^2+4 and g(x)=x+5, find the following

a).(f*g)(x)   b).(f*g)(2)   c).(g*f)(x)    d).(g*f)(2)

myininaya · Answer

f(x)=x^2+4?

myininaya · Answer

*<- this is multiplication?

anonymous · Answer

When you're multiplying functions, you just multiply whatever the function is equal to.  $$(f*g)(x)=(x^2+2)(x+5)$$You just need to foil that to make it work.  Make sure that you're not actually supposed to be doing a COMPOSITION of functions (see the attachment)

myininaya · Answer

(f*g)(x)=f(x)*g(x)
or
do you mean
(f*g)(x)=f(g(x))

myininaya · Answer

* what is the notation you want this to mean?

anonymous · Answer

I think i mean f(g(x))

myininaya · Answer

okay so we will let this be the notation for composition functions
(f*g)(x)=f(g(x))

myininaya · Answer

* eventhough we usually mean to this for multiplication

myininaya · Answer

$$(g*f)(x)=g(f(x))=g(x^2+4)=(x^2+4)+5=x^2+9$$
$$(f*g)(x)=f(g(x))=f(x+5)=(x+5)^2+4=x^2+10x+25+4=x^2+10x+29$$

myininaya · Answer

my thing got cut off at the end

myininaya · Answer

+29 is the ending there

myininaya · Answer

$$g(f(2))=2^2+9=4+9=13$$
i think you can find the last one right?

anonymous · Answer

thank u..

myininaya · Answer

np